Mr Henderson and Ms McConachie travelled to Eternal Spirit – an assisted-dying organisation in Basel, Switzerland – where they were given lethal medication.

They died holding hands on Nov 10.

Dr Erika Preisig, who runs the clinic, said: “The way they went, full of peace and happiness, is amazing. This is what happens when people who live together for a really long time go together."

It is understood the cousins, from Troon in Ayrshire, had planned to take their own lives - with or without assistance.

Dr Preisig travelled to Scotland to meet them and carried out some medical tests a month prior to their deaths.

The pair informed their solicitor of their plans and gave some of their belongings to charity shops, before a member of Eternal Spirit accompanied them to Switzerland, the Sunday Times reports.

British assisted-dying group Friends at the End said their case highlighted the need for a change in UK law to spare the frail and elderly the ordeal of having to travel abroad for assisted death.

Dr Libby Wilson said: “They should have been able to die in their own flat.”

However, Dr Peter Saunders, campaign director of the Care Not Killing alliance, described the cousins’ deaths as “a great tragedy”.

“Assisted suicide in these circumstances is the ultimate abandonment,” he said.

“This tragic case strongly underlines the need for comprehensive and affordable patient-centred care in which people's social and spiritual needs and not just physical needs are provided for."

A bill to legalise assisted dying has been tabled by former Chancellor Lord Falconer in the House of Lords.

The Falconer Bill would make it lawful for doctors to prescribe a fatal dose of drugs to patients thought to have no more than six months to live and who had demonstrated a “clear and settled intention” to end their lives.